"A model of a one-dimensional fluid is investigated in which the praticles [sic] are embedded in a cellular space grid and interact with a modified Lennart-Jones potential. It is shown that with an appropriate change in the potential function the model is also suitable for a two- or three-dimensional fluid with more restricted interactions. The man-fermion-like nature of the system resulting from the hard-rod repulsive part of the modified Lennard-Jones potential makes possible an isomorphism between occupation numbers (number operators) and spin states (spin operators) of an Ising ferromagnet, permitting a convenient mathematical formulation of the problem in terms of the Ising model formalism. While the spinor-algebraic method of Onsager and Kaufman is seen not to lead to a solution of this problem, a method is found for linearizing the partition function which results in a useful series solution. The validity of the solution is first proved by applying it to a one-dimensional model with nearest-neighbor interactions for which the exact partition function is known in closed form. The series solution is shown to offer a convenient and unified method for obtaining, algebraically, correct low-temperature expansions of the partition function for two- and three-dimensional fluids with nearest-neighbor interactions and similar potentials incorporating only a limited number of bonds. Application of the solution to several infinite systems produced consistent and realistic results in various limits and leas to a correct picture of a phase transition under certain conditions without recourse to the Maxwell construction. A numerical evaluation and analysis of the series solution, by means of high-speed computer, for small one-, two-, and three-dimensional systems shows realistic thermodynamic behavior and confirms other estimates of the critical temperature of the three-dimensional system"--Abstract, pages ii-iii.
Lund, Louis H., 1919-1998
Rivers, Jack L.
Willett, Joseph E.
Ph. D. in Physics
University of Missouri at Rolla
xi, 334 pages
© 1968 Ralph Gunter Tross, All rights reserved.
Dissertation - Open Access
Library of Congress Subject Headings
Matrix analytic methods
Print OCLC #
Electronic OCLC #
Link to Catalog Recordhttp://laurel.lso.missouri.edu/record=b1487869~S5
Tross, Ralph G., "Cell model of a fluid with hard-core repulsive long-range attractive potential" (1968). Doctoral Dissertations. 2065.